MinT - Best Known (83−43, 83, s)-Nets in Base 9

Best Known (83−43, 83, s)-Nets in Base 9

(83−43, 83, 98)-Net over F₉ — Constructive and digital

Digital (40, 83, 98)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (6, 27, 34)-net over F₉, using
  - net from sequence [i] based on digital (6, 33)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]
2. digital (13, 56, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(83−43, 83, 147)-Net over F₉ — Digital

Digital (40, 83, 147)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(83−43, 83, 5761)-Net in Base 9 — Upper bound on s

There is no (40, 83, 5762)-net in base 9, because

1 times m-reduction [i] would yield (40, 82, 5762)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 772279 672104 418661 424079 248397 913162 100973 429607 072786 711021 778684 967719 756497 > 9⁸² [i]